Solve 5(x-4)-3(3x+5)-6x^2=4(x-3)-6(x-1)^2+3

$$5 ( x - 4 ) - 3 ( 3 x + 5 ) - 6 x ^ { 2 } = 4 ( x - 3 ) - 6 ( x - 1 ) ^ { 2 } + 3$$

Solve for x

$$x=-1$$

Steps for Solving Linear Equation

Use the distributive property to multiply 5 by x-4.

$$5x-20-3\left(3x+5\right)-6x^{2}=4\left(x-3\right)-6\left(x-1\right)^{2}+3$$

Use the distributive property to multiply -3 by 3x+5.

$$5x-20-9x-15-6x^{2}=4\left(x-3\right)-6\left(x-1\right)^{2}+3$$

Combine 5x and -9x to get -4x.

$$-4x-20-15-6x^{2}=4\left(x-3\right)-6\left(x-1\right)^{2}+3$$

Subtract 15 from -20 to get -35.

$$-4x-35-6x^{2}=4\left(x-3\right)-6\left(x-1\right)^{2}+3$$

Use the distributive property to multiply 4 by x-3.

$$-4x-35-6x^{2}=4x-12-6\left(x-1\right)^{2}+3$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-1\right)^{2}.

$$-4x-35-6x^{2}=4x-12-6\left(x^{2}-2x+1\right)+3$$

Use the distributive property to multiply -6 by x^{2}-2x+1.

$$-4x-35-6x^{2}=4x-12-6x^{2}+12x-6+3$$

Combine 4x and 12x to get 16x.

$$-4x-35-6x^{2}=16x-12-6x^{2}-6+3$$

Subtract 6 from -12 to get -18.

$$-4x-35-6x^{2}=16x-18-6x^{2}+3$$

Add -18 and 3 to get -15.

$$-4x-35-6x^{2}=16x-15-6x^{2}$$

Subtract 16x from both sides.

$$-4x-35-6x^{2}-16x=-15-6x^{2}$$

Combine -4x and -16x to get -20x.

$$-20x-35-6x^{2}=-15-6x^{2}$$

Add 6x^{2} to both sides.

$$-20x-35-6x^{2}+6x^{2}=-15$$

Combine -6x^{2} and 6x^{2} to get 0.

$$-20x-35=-15$$

Add 35 to both sides.

$$-20x=-15+35$$

Add -15 and 35 to get 20.

$$-20x=20$$

Divide both sides by -20.

$$x=\frac{20}{-20}$$

Divide 20 by -20 to get -1.

$$x=-1$$