Solve for x (complex solution)
x\in \mathrm{C}
Solve for x
x\in \mathrm{R}
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-2x^{2}+19x-42+7=\left(-x+7\right)\left(2x-5\right)
Use the distributive property to multiply -2x+7 by x-6 and combine like terms.
-2x^{2}+19x-35=\left(-x+7\right)\left(2x-5\right)
Add -42 and 7 to get -35.
-2x^{2}+19x-35=2\left(-x\right)x-5\left(-x\right)+14x-35
Use the distributive property to multiply -x+7 by 2x-5.
-2x^{2}+19x-35=2\left(-x\right)x+5x+14x-35
Multiply -5 and -1 to get 5.
-2x^{2}+19x-35=2\left(-x\right)x+19x-35
Combine 5x and 14x to get 19x.
-2x^{2}+19x-35-2\left(-x\right)x=19x-35
Subtract 2\left(-x\right)x from both sides.
-2x^{2}+19x-35-2\left(-x\right)x-19x=-35
Subtract 19x from both sides.
-2x^{2}+19x-35-2\left(-1\right)x^{2}-19x=-35
Multiply x and x to get x^{2}.
-2x^{2}+19x-35+2x^{2}-19x=-35
Multiply -2 and -1 to get 2.
19x-35-19x=-35
Combine -2x^{2} and 2x^{2} to get 0.
-35=-35
Combine 19x and -19x to get 0.
\text{true}
Compare -35 and -35.
x\in \mathrm{C}
This is true for any x.
-2x^{2}+19x-42+7=\left(-x+7\right)\left(2x-5\right)
Use the distributive property to multiply -2x+7 by x-6 and combine like terms.
-2x^{2}+19x-35=\left(-x+7\right)\left(2x-5\right)
Add -42 and 7 to get -35.
-2x^{2}+19x-35=2\left(-x\right)x-5\left(-x\right)+14x-35
Use the distributive property to multiply -x+7 by 2x-5.
-2x^{2}+19x-35=2\left(-x\right)x+5x+14x-35
Multiply -5 and -1 to get 5.
-2x^{2}+19x-35=2\left(-x\right)x+19x-35
Combine 5x and 14x to get 19x.
-2x^{2}+19x-35-2\left(-x\right)x=19x-35
Subtract 2\left(-x\right)x from both sides.
-2x^{2}+19x-35-2\left(-x\right)x-19x=-35
Subtract 19x from both sides.
-2x^{2}+19x-35-2\left(-1\right)x^{2}-19x=-35
Multiply x and x to get x^{2}.
-2x^{2}+19x-35+2x^{2}-19x=-35
Multiply -2 and -1 to get 2.
19x-35-19x=-35
Combine -2x^{2} and 2x^{2} to get 0.
-35=-35
Combine 19x and -19x to get 0.
\text{true}
Compare -35 and -35.
x\in \mathrm{R}
This is true for any x.
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Limits
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