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

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

Solve for x

$$x=\frac{3}{14}\approx 0.214285714$$

Steps for Solving Linear Equation

Use the distributive property to multiply 1+2x by 4+3x and combine like terms.

$$4+11x+6x^{2}=\left(2-x\right)\left(5-6x\right)$$

Use the distributive property to multiply 2-x by 5-6x and combine like terms.

$$4+11x+6x^{2}=10-17x+6x^{2}$$

Add 17x to both sides.

$$4+11x+6x^{2}+17x=10+6x^{2}$$

Combine 11x and 17x to get 28x.

$$4+28x+6x^{2}=10+6x^{2}$$

Subtract 6x^{2} from both sides.

$$4+28x+6x^{2}-6x^{2}=10$$

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

$$4+28x=10$$

Subtract 4 from both sides.

$$28x=10-4$$

Subtract 4 from 10 to get 6.

$$28x=6$$

Divide both sides by 28.

$$x=\frac{6}{28}$$

Reduce the fraction \frac{6}{28} to lowest terms by extracting and canceling out 2.

$$x=\frac{3}{14}$$