Solve (3k - 7)(k - 1) = (5 + k)(3k - 14) | 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

$$(3k-7)\cdot(k-1)=(5+k)\cdot(3k-14)$$

Solve for k

$k=7$

Steps for Solving Linear Equation

Use the distributive property to multiply $3k-7$ by $k-1$ and combine like terms.

$$3k^{2}-10k+7=\left(5+k\right)\left(3k-14\right)$$

Use the distributive property to multiply $5+k$ by $3k-14$ and combine like terms.

$$3k^{2}-10k+7=k-70+3k^{2}$$

Subtract $k$ from both sides.

$$3k^{2}-10k+7-k=-70+3k^{2}$$

Combine $-10k$ and $-k$ to get $-11k$.

$$3k^{2}-11k+7=-70+3k^{2}$$

Subtract $3k^{2}$ from both sides.

$$3k^{2}-11k+7-3k^{2}=-70$$

Combine $3k^{2}$ and $-3k^{2}$ to get $0$.

$$-11k+7=-70$$

Subtract $7$ from both sides.

$$-11k=-70-7$$

Subtract $7$ from $-70$ to get $-77$.

$$-11k=-77$$

Divide both sides by $-11$.

$$k=\frac{-77}{-11}$$

Divide $-77$ by $-11$ to get $7$.

$$k=7$$