Solve (3x - 1)(12x + 1) - 10 = (6x + 2) ^ 2 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(3x-1)(12x+1)-10=(6x+2)^{2}$$

Solve for x

$x=-\frac{5}{11}\approx -0.454545455$

Steps for Solving Linear Equation

Use the distributive property to multiply $3x-1$ by $12x+1$ and combine like terms.

$$36x^{2}-9x-1-10=\left(6x+2\right)^{2}$$

Subtract $10$ from $-1$ to get $-11$.

$$36x^{2}-9x-11=\left(6x+2\right)^{2}$$

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(6x+2\right)^{2}$.

$$36x^{2}-9x-11=36x^{2}+24x+4$$

Subtract $36x^{2}$ from both sides.

$$36x^{2}-9x-11-36x^{2}=24x+4$$

Combine $36x^{2}$ and $-36x^{2}$ to get $0$.

$$-9x-11=24x+4$$

Subtract $24x$ from both sides.

$$-9x-11-24x=4$$

Combine $-9x$ and $-24x$ to get $-33x$.

$$-33x-11=4$$

Add $11$ to both sides.

$$-33x=4+11$$

Add $4$ and $11$ to get $15$.

$$-33x=15$$

Divide both sides by $-33$.

$$x=\frac{15}{-33}$$

Reduce the fraction $\frac{15}{-33}$ to lowest terms by extracting and canceling out $3$.

$$x=-\frac{5}{11}$$